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On cobordism maps on
periodic Floer homology
Guanheng Chen |
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Algebraic & Geometric Topology 21 (2021) 1–103
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Abstract |
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We investigate the cobordism maps on periodic Floer homology (PFH). In the first part of the paper, we define the cobordism maps on PFH via Seiberg–Witten theory as well as the isomorphism between PFH and Seiberg–Witten cohomology. Furthermore, we show that the maps satisfy the holomorphic curve axiom. In the second part of the paper, we give an alternative definition of these maps by using holomorphic curves, provided that the symplectic cobordisms are Lefschetz fibrations satisfying certain nice conditions. Under certain additional monotonicity assumptions, we show that these two definitions are equivalent. |
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Keywords
periodic Floer homology, Seiberg–Witten Floer homology,
cobordism maps
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Mathematical Subject Classification 2010
Primary: 57R58
Secondary: 53D40
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References |
Publication
Received: 23 May 2018
Revised: 29 March 2020
Accepted: 30 March 2020
Published: 25 February 2021
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Authors |
| Guanheng Chen | |
| Department of Mathematics The Chinese University of Hong Kong Hong Kong |
School of Mathematical
Sciences University of Adelaide Adelaide SA Australia |
